The robust stability study of the classic Smith predictor-based control system for uncertain fractional-order plants with interval time delays and interval coefficients is the emphasis of this work.Interval uncertaint...The robust stability study of the classic Smith predictor-based control system for uncertain fractional-order plants with interval time delays and interval coefficients is the emphasis of this work.Interval uncertainties are a type of parametric uncertainties that cannot be avoided when modeling real-world plants.Also,in the considered Smith predictor control structure it is supposed that the controller is a fractional-order proportional integral derivative(FOPID)controller.To the best of the authors'knowledge,no method has been developed until now to analyze the robust stability of a Smith predictor based fractional-order control system in the presence of the simultaneous uncertainties in gain,time-constants,and time delay.The three primary contributions of this study are as follows:ⅰ)a set of necessary and sufficient conditions is constructed using a graphical method to examine the robust stability of a Smith predictor-based fractionalorder control system—the proposed method explicitly determines whether or not the FOPID controller can robustly stabilize the Smith predictor-based fractional-order control system;ⅱ)an auxiliary function as a robust stability testing function is presented to reduce the computational complexity of the robust stability analysis;andⅲ)two auxiliary functions are proposed to achieve the control requirements on the disturbance rejection and the noise reduction.Finally,four numerical examples and an experimental verification are presented in this study to demonstrate the efficacy and significance of the suggested technique.展开更多
Although some numerical methods of the fractional-order chaotic systems have been announced,high-precision numerical methods have always been the direction that researchers strive to pursue.Based on this problem,this ...Although some numerical methods of the fractional-order chaotic systems have been announced,high-precision numerical methods have always been the direction that researchers strive to pursue.Based on this problem,this paper introduces a high-precision numerical approach.Some complex dynamic behavior of fractional-order Lorenz chaotic systems are shown by using the present method.We observe some novel dynamic behavior in numerical experiments which are unlike any that have been previously discovered in numerical experiments or theoretical studies.We investigate the influence of α_(1),α_(2),α_(3) on the numerical solution of fractional-order Lorenz chaotic systems.The simulation results of integer order are in good agreement with those of othermethods.The simulation results of numerical experiments demonstrate the effectiveness of the present method.展开更多
In this paper, a very simple synchronization method is presented for a class of fractional-order chaotic systems only via feedback control. The synchronization technique, based on the stability theory of fractional-or...In this paper, a very simple synchronization method is presented for a class of fractional-order chaotic systems only via feedback control. The synchronization technique, based on the stability theory of fractional-order systems, is simple and theoretically rigorous.展开更多
This paper addresses the robust admissibility problem in singular fractional-order continuous time systems. It is based on new admissibility conditions of singular fractional-order systems expressed in a set of strict...This paper addresses the robust admissibility problem in singular fractional-order continuous time systems. It is based on new admissibility conditions of singular fractional-order systems expressed in a set of strict linear matrix inequalities(LMIs). Then, a static output feedback controller is designed for the uncertain closed-loop system to be admissible. Numerical examples are given to illustrate the proposed methods.展开更多
This paper investigates the function projective synchronization between fractional-order chaotic systems and integer-order chaotic systems using the stability theory of fractional-order systems. The function projectiv...This paper investigates the function projective synchronization between fractional-order chaotic systems and integer-order chaotic systems using the stability theory of fractional-order systems. The function projective synchronization between three-dimensional (3D) integer-order Lorenz chaotic system and 3D fractional-order Chen chaotic system are presented to demonstrate the effectiveness of the proposed scheme.展开更多
In this paper, the leader-following tracking problem of fractional-order multi-agent systems is addressed. The dynamics of each agent may be heterogeneous and has unknown nonlinearities. By assumptions that the intera...In this paper, the leader-following tracking problem of fractional-order multi-agent systems is addressed. The dynamics of each agent may be heterogeneous and has unknown nonlinearities. By assumptions that the interaction topology is undirected and connected and the unknown nonlinear uncertain dynamics can be parameterized by a neural network, an adaptive learning law is proposed to deal with unknown nonlinear dynamics, based on which a kind of cooperative tracking protocols are constructed. The feedback gain matrix is obtained to solve an algebraic Riccati equation. To construct the fully distributed cooperative tracking protocols, the adaptive law is also adopted to adjust the coupling weight. With the developed control laws,we can prove that all signals in the closed-loop systems are guaranteed to be uniformly ultimately bounded. Finally, a simple simulation example is provided to illustrate the established result.展开更多
In this paper, an impulsive synchronisation scheme for a class of fractional-order hyperchaotic systems is proposed. The sufficient conditions of a class of integral-order hyperchaotic systems' impulsive synchronisat...In this paper, an impulsive synchronisation scheme for a class of fractional-order hyperchaotic systems is proposed. The sufficient conditions of a class of integral-order hyperchaotic systems' impulsive synchronisation are illustrated. Furthermore, we apply the sufficient conditions to a class of fractional-order hyperchaotic systems and well achieve impulsive synchronisation of these fractional-order hyperchaotic systems, thereby extending the applicable scope of impulsive synchronisation. Numerical simulations further demonstrate the feasibility and effectiveness of the proposed scheme.展开更多
A no-chattering sliding mode control strategy for a class of fractional-order chaotic systems is proposed in this paper. First, the sliding mode control law is derived to stabilize the states of the commensurate fract...A no-chattering sliding mode control strategy for a class of fractional-order chaotic systems is proposed in this paper. First, the sliding mode control law is derived to stabilize the states of the commensurate fractional-order chaotic system and the non-commensurate fractional-order chaotic system, respectively. The designed control scheme guarantees the asymptotical stability of an uncertain fractional-order chaotic system. Simulation results are given for several fractional-order chaotic examples to illustrate the effectiveness of the proposed scheme.展开更多
The stability of impulsive fractional-order systems is discussed. A new synchronization criterion of fractional-order chaotic systems is proposed based on the stability theory of impulsive fractional-order systems. Th...The stability of impulsive fractional-order systems is discussed. A new synchronization criterion of fractional-order chaotic systems is proposed based on the stability theory of impulsive fractional-order systems. The synchronization criterion is suitable for the case of the order 0 〈 q ≤ 1. It is more general than those of the known results. Simulation results are given to show the effectiveness of the proposed synchronization criterion.展开更多
A challenging topic in nonlinear dynamics concerns the study of fractional-order systems without equilibrium points.In particular, no paper has been published to date regarding the presence of hyperchaos in these syst...A challenging topic in nonlinear dynamics concerns the study of fractional-order systems without equilibrium points.In particular, no paper has been published to date regarding the presence of hyperchaos in these systems. This paper aims to bridge the gap by introducing a new example of fractional-order hyperchaotic system without equilibrium points. The conducted analysis shows that hyperchaos exists in the proposed system when its order is as low as 3.84. Moreover, an interesting application of hyperchaotic synchronization to the considered fractional-order system is provided.展开更多
In this paper, we propose a robust fractional-order proportional-integral(FOPI) observer for the synchronization of nonlinear fractional-order chaotic systems. The convergence of the observer is proved, and sufficient...In this paper, we propose a robust fractional-order proportional-integral(FOPI) observer for the synchronization of nonlinear fractional-order chaotic systems. The convergence of the observer is proved, and sufficient conditions are derived in terms of linear matrix inequalities(LMIs) approach by using an indirect Lyapunov method. The proposed FOPI observer is robust against Lipschitz additive nonlinear uncertainty. It is also compared to the fractional-order proportional(FOP) observer and its performance is illustrated through simulations done on the fractional-order chaotic Lorenz system.展开更多
This study explores a stable model order reduction method for fractional-order systems. Using the unsymmetric Lanczos algorithm, the reduced order system with a certain number of matched moments is generated. To obtai...This study explores a stable model order reduction method for fractional-order systems. Using the unsymmetric Lanczos algorithm, the reduced order system with a certain number of matched moments is generated. To obtain a stable reduced order system, the stable model order reduction procedure is discussed. By the revised operation on the tridiagonal matrix produced by the unsymmetric Lanczos algorithm, we propose a reduced order modeling method for a fractional-order system to achieve a satisfactory fitting effect with the original system by the matched moments in the frequency domain. Besides, the bound function of the order reduction error is offered. Two numerical examples are presented to illustrate the effectiveness of the proposed method.展开更多
For a class of fractional-order linear continuous-time switched systems specified by an arbitrary switching sequence,the performance of PDα-type fractional-order iterative learning control(FOILC)is discussed in the s...For a class of fractional-order linear continuous-time switched systems specified by an arbitrary switching sequence,the performance of PDα-type fractional-order iterative learning control(FOILC)is discussed in the sense of L^p norm.When the systems are disturbed by bounded external noises,robustness of the PDα-type algorithm is firstly analyzed in the iteration domain by taking advantage of the generalized Young inequality of convolution integral.Then,convergence of the algorithm is discussed for the systems without any external noise.The results demonstrate that,under some given conditions,both convergence and robustness can be guaranteed during the entire time interval.Simulations support the correctness of the theory.展开更多
Based on the idea of tracking control and stability theory of fractional-order systems, a controller is designed to synchronize the fractional-order chaotic system with chaotic systems of integer orders, and synchroni...Based on the idea of tracking control and stability theory of fractional-order systems, a controller is designed to synchronize the fractional-order chaotic system with chaotic systems of integer orders, and synchronize the different fractional-order chaotic systems. The proposed synchronization approach in this paper shows that the synchronization between fractional-order chaotic systems and chaotic systems of integer orders can be achieved, and the synchronization between different fractional-order chaotic systems can also be realized. Numerical experiments show that the present method works very well.展开更多
This paper addresses improvements in fractional order(FO)system performance.Although the classical proportional-integral-derivative(PID)-like fuzzy controller can provide adequate results for both transient and steady...This paper addresses improvements in fractional order(FO)system performance.Although the classical proportional-integral-derivative(PID)-like fuzzy controller can provide adequate results for both transient and steady-state responses in both linear and nonlinear systems,the FOPID fuzzy controller has been proven to provide better results.This high performance was obtained thanks to the combinative benefits of FO and fuzzy-logic techniques.This paper describes how the optimal gains and FO parameters of the FOPID controller were obtained by the use of a modern optimizer,social spider optimization,in order to improve the response of fractional dynamical systems.This group of systems had usually produced multimodal error surfaces/functions that occasionally had many variant local minima.The integral time of absolute error(ITAE)used in this study was the error function.The results showed that the strategy adopted produced superior performance regarding the lowest ITAE value.It reached a value of 88.22 while the best value obtained in previous work was 98.87.A further comparison between the current work and previous studies concerning transient-analysis factors of the model’s response showed that the strategy proposed was the only one that was able to produce fast rise time,low-percentage overshoot,and very small steady-state error.However,the other strategies were good for one factor,but not for the others.展开更多
The controllability for a class of fractional-order linear control systems is mainly investigated. The generalizations of the usual complete solution formulae of the fractional-order linear control systems are derived...The controllability for a class of fractional-order linear control systems is mainly investigated. The generalizations of the usual complete solution formulae of the fractional-order linear control systems are derived not only for time-invariant case but also for time-varying case. Several sufficient and necessary conditions for state controllability of such systems are established and the corresponding criteria for fractional-order time-invariant continuous-time systems are also obtained. The results obtained will be help for future study of fractional-order control systems.展开更多
A specific state variable in a class of 3D continuous fractional-order chaotic systems is presented. All state variables of fractional-order chaotic systems of this class can be obtained via a specific state variable ...A specific state variable in a class of 3D continuous fractional-order chaotic systems is presented. All state variables of fractional-order chaotic systems of this class can be obtained via a specific state variable and its (q-order and 2q-order) time derivatives. This idea is demonstrated by using several well-known fractional-order chaotic systems. Finally, a synchronization scheme is investigated for this fractional-order chaotic system via a specific state variable and its (q-order and 2q-order) time derivatives. Some examples are used to illustrate the effectiveness of the proposed synchronization method.展开更多
This paper presents a modified sliding mode control for fractional-order chaotic economical systems with parameter uncertainty and external disturbance. By constructing the suitable sliding mode surface with fractiona...This paper presents a modified sliding mode control for fractional-order chaotic economical systems with parameter uncertainty and external disturbance. By constructing the suitable sliding mode surface with fractional-order integral, the effective sliding mode controller is designed to realize the asymptotical stability of fractional-order chaotic economical systems. Comparing with the existing results, the main results in this paper are more practical and rigorous. Simulation results show the effectiveness and feasibility of the proposed sliding mode control method.展开更多
This paper proposes a new chaotic system and its fractional-order chaotic system. The necessary condition for the existence of chaotic attractors in this new fractional-order system is obtained. It finds that this new...This paper proposes a new chaotic system and its fractional-order chaotic system. The necessary condition for the existence of chaotic attractors in this new fractional-order system is obtained. It finds that this new fractional-order system is chaotic for q 〉 0.783 if the system parameter m=6. The chaotic attractors for q=0.8, and q=0.9 are obtained. A circuit is designed to realize its fractional-order chaos system for q=0.9 by electronic workbench.展开更多
Modularized circuit designs for chaotic systems are introduced in this paper.Especially,a typical improved modularized design strategy is proposed and applied to a new hyper-chaotic system circuit implementation.In th...Modularized circuit designs for chaotic systems are introduced in this paper.Especially,a typical improved modularized design strategy is proposed and applied to a new hyper-chaotic system circuit implementation.In this paper,the detailed design procedures are described.Multisim simulations and physical experiments are conducted,and the simulation results are compared with Matlab simulation results for different system parameter pairs.These results are consistent with each other and they verify the existence of the hyper-chaotic attractor for this new hyper-chaotic system.展开更多
基金supported by the Estonian Research Council(PRG658)。
文摘The robust stability study of the classic Smith predictor-based control system for uncertain fractional-order plants with interval time delays and interval coefficients is the emphasis of this work.Interval uncertainties are a type of parametric uncertainties that cannot be avoided when modeling real-world plants.Also,in the considered Smith predictor control structure it is supposed that the controller is a fractional-order proportional integral derivative(FOPID)controller.To the best of the authors'knowledge,no method has been developed until now to analyze the robust stability of a Smith predictor based fractional-order control system in the presence of the simultaneous uncertainties in gain,time-constants,and time delay.The three primary contributions of this study are as follows:ⅰ)a set of necessary and sufficient conditions is constructed using a graphical method to examine the robust stability of a Smith predictor-based fractionalorder control system—the proposed method explicitly determines whether or not the FOPID controller can robustly stabilize the Smith predictor-based fractional-order control system;ⅱ)an auxiliary function as a robust stability testing function is presented to reduce the computational complexity of the robust stability analysis;andⅲ)two auxiliary functions are proposed to achieve the control requirements on the disturbance rejection and the noise reduction.Finally,four numerical examples and an experimental verification are presented in this study to demonstrate the efficacy and significance of the suggested technique.
基金supported by the Natural Science Foundation of Inner Mongolia[2021MS01009]Jining Normal University[JSJY2021040,Jsbsjj1704,jsky202145].
文摘Although some numerical methods of the fractional-order chaotic systems have been announced,high-precision numerical methods have always been the direction that researchers strive to pursue.Based on this problem,this paper introduces a high-precision numerical approach.Some complex dynamic behavior of fractional-order Lorenz chaotic systems are shown by using the present method.We observe some novel dynamic behavior in numerical experiments which are unlike any that have been previously discovered in numerical experiments or theoretical studies.We investigate the influence of α_(1),α_(2),α_(3) on the numerical solution of fractional-order Lorenz chaotic systems.The simulation results of integer order are in good agreement with those of othermethods.The simulation results of numerical experiments demonstrate the effectiveness of the present method.
文摘In this paper, a very simple synchronization method is presented for a class of fractional-order chaotic systems only via feedback control. The synchronization technique, based on the stability theory of fractional-order systems, is simple and theoretically rigorous.
文摘This paper addresses the robust admissibility problem in singular fractional-order continuous time systems. It is based on new admissibility conditions of singular fractional-order systems expressed in a set of strict linear matrix inequalities(LMIs). Then, a static output feedback controller is designed for the uncertain closed-loop system to be admissible. Numerical examples are given to illustrate the proposed methods.
文摘This paper investigates the function projective synchronization between fractional-order chaotic systems and integer-order chaotic systems using the stability theory of fractional-order systems. The function projective synchronization between three-dimensional (3D) integer-order Lorenz chaotic system and 3D fractional-order Chen chaotic system are presented to demonstrate the effectiveness of the proposed scheme.
基金supported by the National Natural Science Foundation of China(61303211)Zhejiang Provincial Natural Science Foundation of China(LY17F030003,LY15F030009)
文摘In this paper, the leader-following tracking problem of fractional-order multi-agent systems is addressed. The dynamics of each agent may be heterogeneous and has unknown nonlinearities. By assumptions that the interaction topology is undirected and connected and the unknown nonlinear uncertain dynamics can be parameterized by a neural network, an adaptive learning law is proposed to deal with unknown nonlinear dynamics, based on which a kind of cooperative tracking protocols are constructed. The feedback gain matrix is obtained to solve an algebraic Riccati equation. To construct the fully distributed cooperative tracking protocols, the adaptive law is also adopted to adjust the coupling weight. With the developed control laws,we can prove that all signals in the closed-loop systems are guaranteed to be uniformly ultimately bounded. Finally, a simple simulation example is provided to illustrate the established result.
基金supported by the National Natural Science Foundation of China (Grant Nos. 60573172 and 60973152)the Doctoral Program Foundation of the Institution of Higher Education of China (Grant No. 20070141014)the Natural Science Foundation of Liaoning Province,China (No. 20082165)
文摘In this paper, an impulsive synchronisation scheme for a class of fractional-order hyperchaotic systems is proposed. The sufficient conditions of a class of integral-order hyperchaotic systems' impulsive synchronisation are illustrated. Furthermore, we apply the sufficient conditions to a class of fractional-order hyperchaotic systems and well achieve impulsive synchronisation of these fractional-order hyperchaotic systems, thereby extending the applicable scope of impulsive synchronisation. Numerical simulations further demonstrate the feasibility and effectiveness of the proposed scheme.
基金supported by the National Natural Science Foundation of China (Grant No. 51109180)the Personal Special Fund of Northwest Agriculture and Forestry University,China (Grant No. RCZX-2009-01)
文摘A no-chattering sliding mode control strategy for a class of fractional-order chaotic systems is proposed in this paper. First, the sliding mode control law is derived to stabilize the states of the commensurate fractional-order chaotic system and the non-commensurate fractional-order chaotic system, respectively. The designed control scheme guarantees the asymptotical stability of an uncertain fractional-order chaotic system. Simulation results are given for several fractional-order chaotic examples to illustrate the effectiveness of the proposed scheme.
基金supported by Scientific Research Foundation of Huaiyin Institute of Technology (Grant No. HGA1102)
文摘The stability of impulsive fractional-order systems is discussed. A new synchronization criterion of fractional-order chaotic systems is proposed based on the stability theory of impulsive fractional-order systems. The synchronization criterion is suitable for the case of the order 0 〈 q ≤ 1. It is more general than those of the known results. Simulation results are given to show the effectiveness of the proposed synchronization criterion.
文摘A challenging topic in nonlinear dynamics concerns the study of fractional-order systems without equilibrium points.In particular, no paper has been published to date regarding the presence of hyperchaos in these systems. This paper aims to bridge the gap by introducing a new example of fractional-order hyperchaotic system without equilibrium points. The conducted analysis shows that hyperchaos exists in the proposed system when its order is as low as 3.84. Moreover, an interesting application of hyperchaotic synchronization to the considered fractional-order system is provided.
基金supported by King Abdullah University of Science and Technology (KAUST),KSA
文摘In this paper, we propose a robust fractional-order proportional-integral(FOPI) observer for the synchronization of nonlinear fractional-order chaotic systems. The convergence of the observer is proved, and sufficient conditions are derived in terms of linear matrix inequalities(LMIs) approach by using an indirect Lyapunov method. The proposed FOPI observer is robust against Lipschitz additive nonlinear uncertainty. It is also compared to the fractional-order proportional(FOP) observer and its performance is illustrated through simulations done on the fractional-order chaotic Lorenz system.
基金supported by the National Natural Science Foundation of China(61304094,61673198,61773187)the Natural Science Foundation of Liaoning Province,China(20180520009)
文摘This study explores a stable model order reduction method for fractional-order systems. Using the unsymmetric Lanczos algorithm, the reduced order system with a certain number of matched moments is generated. To obtain a stable reduced order system, the stable model order reduction procedure is discussed. By the revised operation on the tridiagonal matrix produced by the unsymmetric Lanczos algorithm, we propose a reduced order modeling method for a fractional-order system to achieve a satisfactory fitting effect with the original system by the matched moments in the frequency domain. Besides, the bound function of the order reduction error is offered. Two numerical examples are presented to illustrate the effectiveness of the proposed method.
基金supported by the National Natural Science Foundation of China(61201323)the Special Fund Project for Promoting Scientific and Technological Innovation in Xuzhou City(KC18013)the Cultivation Project of Xuzhou Institute of Technology(XKY2017112)
文摘For a class of fractional-order linear continuous-time switched systems specified by an arbitrary switching sequence,the performance of PDα-type fractional-order iterative learning control(FOILC)is discussed in the sense of L^p norm.When the systems are disturbed by bounded external noises,robustness of the PDα-type algorithm is firstly analyzed in the iteration domain by taking advantage of the generalized Young inequality of convolution integral.Then,convergence of the algorithm is discussed for the systems without any external noise.The results demonstrate that,under some given conditions,both convergence and robustness can be guaranteed during the entire time interval.Simulations support the correctness of the theory.
基金supported by the Education Committee of Chongqing Province,China (Grant No.KJ090503)
文摘Based on the idea of tracking control and stability theory of fractional-order systems, a controller is designed to synchronize the fractional-order chaotic system with chaotic systems of integer orders, and synchronize the different fractional-order chaotic systems. The proposed synchronization approach in this paper shows that the synchronization between fractional-order chaotic systems and chaotic systems of integer orders can be achieved, and the synchronization between different fractional-order chaotic systems can also be realized. Numerical experiments show that the present method works very well.
文摘This paper addresses improvements in fractional order(FO)system performance.Although the classical proportional-integral-derivative(PID)-like fuzzy controller can provide adequate results for both transient and steady-state responses in both linear and nonlinear systems,the FOPID fuzzy controller has been proven to provide better results.This high performance was obtained thanks to the combinative benefits of FO and fuzzy-logic techniques.This paper describes how the optimal gains and FO parameters of the FOPID controller were obtained by the use of a modern optimizer,social spider optimization,in order to improve the response of fractional dynamical systems.This group of systems had usually produced multimodal error surfaces/functions that occasionally had many variant local minima.The integral time of absolute error(ITAE)used in this study was the error function.The results showed that the strategy adopted produced superior performance regarding the lowest ITAE value.It reached a value of 88.22 while the best value obtained in previous work was 98.87.A further comparison between the current work and previous studies concerning transient-analysis factors of the model’s response showed that the strategy proposed was the only one that was able to produce fast rise time,low-percentage overshoot,and very small steady-state error.However,the other strategies were good for one factor,but not for the others.
文摘The controllability for a class of fractional-order linear control systems is mainly investigated. The generalizations of the usual complete solution formulae of the fractional-order linear control systems are derived not only for time-invariant case but also for time-varying case. Several sufficient and necessary conditions for state controllability of such systems are established and the corresponding criteria for fractional-order time-invariant continuous-time systems are also obtained. The results obtained will be help for future study of fractional-order control systems.
文摘A specific state variable in a class of 3D continuous fractional-order chaotic systems is presented. All state variables of fractional-order chaotic systems of this class can be obtained via a specific state variable and its (q-order and 2q-order) time derivatives. This idea is demonstrated by using several well-known fractional-order chaotic systems. Finally, a synchronization scheme is investigated for this fractional-order chaotic system via a specific state variable and its (q-order and 2q-order) time derivatives. Some examples are used to illustrate the effectiveness of the proposed synchronization method.
基金supported by the National Natural Science Foundation of China(Grant Nos.51207173 and 51277192)
文摘This paper presents a modified sliding mode control for fractional-order chaotic economical systems with parameter uncertainty and external disturbance. By constructing the suitable sliding mode surface with fractional-order integral, the effective sliding mode controller is designed to realize the asymptotical stability of fractional-order chaotic economical systems. Comparing with the existing results, the main results in this paper are more practical and rigorous. Simulation results show the effectiveness and feasibility of the proposed sliding mode control method.
基金supported by Chongqing Education Committee of China (Grant No KJ070502)
文摘This paper proposes a new chaotic system and its fractional-order chaotic system. The necessary condition for the existence of chaotic attractors in this new fractional-order system is obtained. It finds that this new fractional-order system is chaotic for q 〉 0.783 if the system parameter m=6. The chaotic attractors for q=0.8, and q=0.9 are obtained. A circuit is designed to realize its fractional-order chaos system for q=0.9 by electronic workbench.
基金supported by the Young Scientists Fund of the National Natural Science Foundation of China(Grant No.61403395)the Natural Science Foundation of Tianjin,China(Grant No.13JCYBJC39000)+3 种基金the Scientific Research Foundation for the Returned Overseas Chinese Scholars,State Education Ministry of Chinathe Fund from the Tianjin Key Laboratory of Civil Aircraft Airworthiness and Maintenance in Civil Aviation of China(Grant No.104003020106)the National Basic Research Program of China(Grant No.2014CB744904)the Fund for the Scholars of Civil Aviation University of China(Grant No.2012QD21x)
文摘Modularized circuit designs for chaotic systems are introduced in this paper.Especially,a typical improved modularized design strategy is proposed and applied to a new hyper-chaotic system circuit implementation.In this paper,the detailed design procedures are described.Multisim simulations and physical experiments are conducted,and the simulation results are compared with Matlab simulation results for different system parameter pairs.These results are consistent with each other and they verify the existence of the hyper-chaotic attractor for this new hyper-chaotic system.